Ok, I had two identic routers, Fritzbox 3970, one running as router and the other as access point. The AP is connected to the router with a network cable. On both devices I had WIFI active, with the same SSID but different channels. So my mobile devices could connect to the nearest WIFI station. This worked fine.
At a weekend I replaced the router one by a newer model: Fritzbox 7490. About this weekend I updated my iOS devices to 8.4.1.
Some days after the weekend, I found out Airplay does not work any more and thought it's a problem of iOS.
Now I found out, if I use different SSIDs (in my two Fritzboxes) Airplay works fine. Now I have to setup two WIFI configurations in my mobile devices.